If you have sometimes noticed someone familiar in a crowd when not scanning for them and sometimes not noticed familiar faces in a crowd in similar circumstance then I propose such discovery is neither automatic nor is it tied to a specific action or intent on the observer.
I have noticed friends and family where I didn't expect to see them. I have failed to notice friends and family where I didn't expect to see them. I know because they noticed me and said hello. Such discovery does not force an interaction: it offers a possibility for a choice that didn't exist a moment ago. I know I have decided to say hello sometimes and decided to remain apart others. I presumes those who noticed me made similar choices.
I have noticed and stopped an attempted pickpocket whilst thinking about nothing more than enjoying the concert. I certainly wasn't guardedly protecting myself.
Observation and perceptiveness act passively. One can improve one's chances of success by specifically looking for a certain thing (and as the gorilla experiment shows such concentration impairs other perception's chances of being noticed).
It should not be tied to an action. It should be based on a fortune mechanic check, preferably tied to however perceptiveness is mechanically expressed in the game.
I've never found examples from "real life" to be very compelling arguments when discussing D&D in part because it is a game with particular rules that aren't the same as the rules that apply in "real life."
But let's examine your observations. First, whether a friend or family member in a crowd is noticed by the PC can be decided by the DM without reference to mechanics. The DM simply describes the environment as including said friend or family member. To say that the DM doesn't know whether a PC might notice a friend or family member in the crowd is strange to me. He or she can just decide that he or she does. That is especially so if the DM needs that outcome to happen (perhaps the friend or family member is a quest giver). If the DM
doesn't need that outcome to happen, then this whole example is rather pointless as, so far as I can tell, you're just resolving this with a random number generator that involves no choice on the part of the player except what he or she made in character creation or advancement while at the same time assuming what the character is doing.
As for the pickpocket you thwarted, you weren't tracking, navigating, drawing a map, foraging, etc. in the manner described by the Basic Rules. In game terms, you were staying alert to hidden dangers. As a result, you noticed the pickpocket. You didn't say you were alert to hidden dangers to some other person. You likely didn't think about it at all. But if you're playing in a game with someone who can't say what your character is doing (the DM), you have to say something at some point about what the character is doing while traveling around. To do otherwise is to make the DM assume what your character is doing or, he or she having asked for a check of some kind,
established what the character is doing (keeping watch for danger). You might be perfectly fine with the DM doing that. You might be fine with doing that as DM and your players are good with it. Myself and others are not. We want a say as players. It's our role in the game as players to do that, too. It's the one thing we get to do in the basic conversation of the game. What does it hurt the DM to let us do that?
"Observation and perceptiveness" do not work passively in the game in the same sense as you suggest it does in "real life." If you're staying alert for danger as you travel about, the DM may resolve any uncertainty as to whether you notice that danger with a passive Perception check. "Passive" here refers to there being no dice, not that the character isn't actively doing something. If you're performing some task other than that which is at least as distracting as some of the tasks I mentioned above, then the character has no chance of noticing the danger. (He or she might not have a chance of noticing the danger if he or she is not in the appropriate rank of the marching order.) If a character decides to look for a hidden object or creature (as with the Search action), then the DM may call for a Wisdom (Perception) check to resolve any uncertainty as to the outcome, if there's a meaningful consequence of failure.
Those are the rules of the game. They are not the same as the rules that apply to "real life." Whether you choose to play by the rules of either is up to you and not for me to judge. Unless of course I happen to be sitting at your table and keep having my character's actions established by someone other than me. Then I have to judge whether this is a game I want to continue playing.
